1. Field of the Invention
This invention relates to the processing of geophysical data to render it more useful in interpreting the geophysical characteristics of the earth in the exploration for oil and gas deposits. More specifically, this invention relates to a method for compensating for the effects of earth filtering on seismic data so that later processing of the seismic data may be performed on a more accurate representation of the reflectivity characteristics of the subsurface formation. It should be clearly understood, however, that while the invention will be described with respect to the processing of seismic data, it is equally applicable to other types of geophysical data, such as well logs, gravity information, and magnetic data.
2. Description of the Prior Art
In seismic exploration, data is obtained by first creating an artificial disturbance along the earth by use of dynamite or the like. The resulting acoustic waves travel downwardly in the earth and are reflected upward from subsurface reflecting interfaces. The reflected waves are received at detectors or geophones located along the ground and recorded in reproducible form. Ideally, the waves recorded at the detectors would be exactly representative of the reflection characteristics (referred to as the reflectivity function) of the earth without the presence of any undesirable components, such as noise or distortion.
Unfortunately, the signals recorded at the detectors contain many undesirable components which often obscure the reflectivity function of the earth and prevent the finding of an area of the earth where oil and gas deposits may be present. One undesirable component of the recorded seismic data is due to the seismic disturbance created by the explosion of dynamite and known as the shot pulse. Ideally, the time waveform of the shot pulse should be a simple short pulse, such as an impulse or square wave. Instead, the shot pulse resulting from the explosion of dynamite or almost any other known seismic source, is a complex train of wavelets. As a result, the reflectivity function of the earth is obscured by the complex waveforms of the reflected shot pulse appearing on the recorded data.
Other undesirable components in the seismogram may be referred to collectively as the distortion operator. These include the effect of multiple reflections, ghosts, reverberations, and other types of distortion known in the seismic art. Furthermore, the effect of the distortion operator is intermixed in a complex way with the shot pulse. Therefore, the distortion operator and the shot pulse may be lumped together as a single component and called the distorted shot pulse, or seismic wavelet. It is desirable to remove the effects of the distorted shot pulse on the seismogram, but the difficulty is that the waveform of the distorted shot pulse is unknown.
Also affecting the propagation of seismic waves from the source to the receiver are several other phenomena which causes additional distortion of the received waves. One such phenomenon is absorption. Absorption causes the actual loss of seismic energy by converting it to other forms of energy. This type of loss of seismic energy is generally known as intrinsic attenuation. A second phenomenon is intrabed multiple interference. Intrabed multiple interference redistributes seismic energy between downward and upward directions. This type of loss of seismic energy is generally known as apparent attenuation. Apparent attenuation causes a progressive loss of the higher frequencies (broadening of the seismic wavelet) and an increasing phase distortion with increasing travel time for the seismic wavelet received.
It is this combination of intrinsic and apparent attenuation which is known as the earth filter. As a result of earth filtering, the seismic wavelet is time varying. The existence of a time varying seismic wavelet violates a basic assumption of deconvolution theory and impairs the ability to use deconvolution to determine the earth filter characteristics as part of a method of seismic interpretation.
The traditional method of deconvolution, generally known as the "flat-iron" or the "Wiener-Levinson" deconvolution method, assumes that the seismic wavelet is minimum phase or "front-loaded." It is also assumed the reflectivity function is white (i.e. its amplitude spectrum is constant with frequency.) Under these assumptions, the amplitude spectrum of the wavelet and the amplitude spectrum of the seismic trace are equivalent. Further, once the amplitude spectrum is determined, the phase spectrum can be easily calculated by using the above-mentioned assumption that the wavelet is minimum phase after sampling. Once the seismic wavelet is estimated from the calculated amplitude spectrum and phase spectrum, an inverse filter can be designed to compress the seismic wavelet into a short output wavelet close to a spike. In the actual implementation of the Wiener-Levinson method, the inverse filter is calculated in one step from the autocorrelation of the seismic trace. Since the filter calculated in the Wiener-Levinson method is minimum phase, the output wavelet tends to be minimum phase, instead of zero phase.
A method of processing geophysical data which improved upon the above-described "flat-iron" or "Wiener-Levinson" method was disclosed in U.S. Pat. No. 3,396,365, issued to Clyde W. Kerns for a method of processing geophysical data with stable inverse filters. Kerns discloses a method of processing seismic data to suppress coherent noise such as multiples, reverberations and ghosts. In Kerns, an autocorrelation function is produced from an input seismic signal to characterize the noise. A white spike is added to the center point of the autocorrelation function to assure the stability of an inverse filter which is generated from the autocorrelation function. The input seismic signal is then convolved with the inverse filter to produce a filtered signal with the undesired components suppressed.
The Kerns patent also discloses what has been the traditional solution to the problem of intrinsic and apparent attenuation of the seismic wavelet due to the earth filter. In such traditional solutions, a portion of the input trace, generally referred to as a "window", over which the seismic trace does not vary with respect to time, was selected. Each window would be deconvolved separately. After separate deconvolution of each window, the deconvolved windows would be combined together to form a deconvolved seismic trace.
In contrast to the traditional window approach to compensate for earth filter attenuation, the method of compensating for earth filter attenuation which is the subject of the present invention avoids the prior art window approach by disclosing a method of applying a time varying filter to the seismic trace to produce a stationary trace and then apply traditional deconvolution theory to determine the seismic wavelet. By utilization of the disclosed method, the assumption that the input wavelet does not vary in time, an assumption inherent in the prior art "windowing" methods, would be avoided.
An alternate method of determining the effect of the earth filter on a seismic trace which avoids the time-domain "windowing"techniques of the prior art was disclosed in Q-Adaptive Deconvolution by D. Hale. Hale discloses two iterative procedures for implementing inverse Q-filtering. However, the procedures disclosed by Hale make several assumptions which cause Hale to arrive at an approximate dispersion relationship. Use of the approximate dispersion relationship, in turn, degrades the value of the Q compensation obtained by Hale.
The article entitled Minimum Phase and Related Properties of the Response of a Horizontallv Stratified Absorptive Earth to Plane Acoustic Waves by J. Sherwood and A. Trorey has shown that both linear intrinsic attenuation and apparent attenuation are minimum-phase at least in the one dimensional case. Therefore, the phase distortion .phi.(f) due to the earth filter QF(f) may be obtained as the Hilbert transform of the logarithm of the absolute value of the amplitude spectrum .vertline.QF(f).vertline.. More specifically: ##EQU1##
The phase distortion .phi.(f) appears as dispersion, i.e. a change in phase velocity with frequency.
The publication Quantitative Seismology Theory and Methods, Vol. 1 by K. Aki and P. Richards discusses several models of the earth-filter response which provide for a constant or nearly constant Q over part of or the entire frequency range. More specifically, ##EQU2## where:
c and c.sub.o are the phase velocities at the arbitrary frequencies f and f.sub.o respectively.
One model is provided by the thesis entitled Attenuation of Seismic Waves in Rocks and Applications in Energy Exploration by Einar Kjartansson. According to Kjartansson's model, the phase velocity is given by ##EQU3##
This leads to the same dispersion relation as in equation (3).